Mapping Sandpiles to Complex Networks
Abbas Shoja-Daliklidash, Morteza Nattagh-Najafi, Nasser, Sepehri-Javan

TL;DR
This paper establishes a novel connection between sandpile models in self-organized criticality and complex networks, revealing how network properties depend on similarity parameters and analyzing their structural characteristics.
Contribution
It introduces a similarity-based transfer function linking sandpiles to complex networks and characterizes the resulting network's degree distribution and centrality measures.
Findings
Degree centrality follows a generalized Gamma distribution, transitioning to power-law.
Network density is more sensitive to the filtration parameter $r_2$.
Shannon entropy decreases linearly with $r_2$ and is analytically modeled.
Abstract
In this paper, we address a longstanding challenge in self-organized criticality (SOC) systems: establishing a connection between sandpiles and complex networks. Our approach employs a similarity-based transfer function characterized by two parameters, . Here, quantifies the similarity of local activities, while governs the filtration process used to convert a weighted network into a binary one. We reveal that the degree centrality distribution of the resulting network follows a generalized Gamma distribution (GGD), which transitions to a power-law distribution under specific conditions. The GGD exponents, estimated numerically, exhibit a dependency on . Notably, while both decreasing and lead to denser networks, plays a more significant role in influencing network density. Furthermore, the Shannon entropy is observed to…
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Taxonomy
TopicsGeochemistry and Geologic Mapping
